This simple theoretical analysis of container dissolution, transport, and deposition in a sodium-filled, high-nickel superalloy heat pipe is intended to illustrate some of the issues involved in the application of such alloys to liquid metal heat transport systems such as the heat pipe for the Stirling Space Power Converter. As a first step, a cylindrical heat pipe is considered, but in principle the analysis could be extended to the complex Stirling heat pipe. In the analysis, it has been necessary to adapt corrosion rate data from pumped loops. The numerical results should not be used to form judgments about the feasibility of using superalloys in the system. Rather, they may suggest avenues of experimental investigation into the problem. They may also provide impetus for studying means of control, such as coatings.